A fullerene is a 3-regular plane graph with only hexagonal and pentagonal faces. The Fries number of a fullerene G, F(G), is the maximum number of benzene rings over all possible Kekulé structures for G. The Clar number of G, C(G), is the maximum number of independent benzene rings possible over all possible Kekulé structures for G. In this paper, we show that for leapfrog fullerenes, any set of faces attaining the Clar number is a subset of faces attaining the Fries number. This property is false for fullerenes in general (as shown in paper from E. J. Hartung in 2014). We then show that if L(G) is the leapfrog of a fullerene G, then the Clar number of L(G) is equal to the vertex independence number of G.

Rights

URN

URN:NBN:SI:doc-3MO9Y4EV

COBISS ID

285430787

DOI

10.26493/2820-6657.7.9ae

Added

24.08.2026

Metadata

Citation

APA:

Graver, Jack E., Hartung, Elizabeth J. (2025). Clar numbers of leapfrog fullerenes, volume 1, issue 1, article p1.05. URN:NBN:SI:doc-3MO9Y4EV from http://www.dlib.si

MLA:

Graver, Jack E., Hartung, Elizabeth J.. Clar numbers of leapfrog fullerenes. University of Primorska, 2025.
<http://www.dlib.si/?URN=URN:NBN:SI:doc-3MO9Y4EV>